Question

State the 5 th and 6 th terms of triangular numbers.what square number will get if we add these two numbers?

Answer 1

Hi,

1, 3, 6 , 10, 15 , 21 , 28 , 45,.....

Above sequence shows the a pattern

of dots which form a triangle.

* 1 dot

*
* * 3 dots

*
* *
* * * 6 dots

Formula for n th triangular number:

Tn = [ n (n+1)/2]

1) if n= 5,

The 5th triangular number

=[5 (5+1)]/2

= (5 × 6)/2 = 5×3 =15

2) if n= 6,

The 6th triangular number

= [ 6 ( 6 + 1 )/2 ]

= ( 6 × 7 )/ 2

= 3× 7

= 21

Sum of the 5 th and 6th

Triangular numbers = 15 + 21

= 36

= 6 ^2

Therefore,

Required squared number = 6 ^2

I hope this will useful to you.

******

Answer 2

Answer:Hi,

1, 3, 6 , 10, 15 , 21 , 28 , 45,.....

Above sequence shows the a pattern

of dots which form a triangle.

* 1 dot

*

* * 3 dots

*

* *

* * * 6 dots

Formula for n th triangular number:

Tn = [ n (n+1)/2]

1) if n= 5,

The 5th triangular number

=[5 (5+1)]/2

= (5 × 6)/2 = 5×3 =15

2) if n= 6,

The 6th triangular number

= [ 6 ( 6 + 1 )/2 ]

= ( 6 × 7 )/ 2

= 3× 7

= 21

Sum of the 5 th and 6th

Triangular numbers = 15 + 21

= 36

= 6 ^2

Therefore,

Required squared number = 6 ^2

I hope this will useful to you.